(Putting on a flame retardant suit...)
As far as Santana goes, I believe that he's a phenomenal guitarist, but in thinking about it, I'm not sure he would qualify under my 'definition' of a musician.
If given an appropriate amount of time to become familiar with a style of music, would a player be able to transition seamlessly into that style, without necessarily drawing attention to themselves.
Use Carole Kaye as an example.
Can she play jazz? Pop? Country? Blues? Rock? The answer to all of these are yes, and she never did anything but play the required lines very well. I've never heard her play metal, but I'm confident because of her track record, that she could study it and find the appropriate lines, using her knowledge and technical abilities. And she never brought the spotlight onto herself.
Growing up, I've heard Vai play jazz, rock, metal and pop. I've seen him cop fingerpicked lines like a country guitarist. In his solo stuff, he's like Carlos, in that he sounds like himself. But I've never heard Carlos show that flexibility.
Mind you, I'm not up on all of his past recordings, whereas I listened to a ton of Vai, so I may be wrong.
But, in retrospect, everything that I've heard Santana play, sounds like Santana playing Santana.
A musician is a chameleon, able to make themselves disappear into the music. The first call studio guys are very adept at this.